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Oscillations In An LC Circuit01:30

Oscillations In An LC Circuit

2.7K
An idealized LC circuit of zero resistance can oscillate without any source of emf by shifting the energy stored in the circuit between the electric and magnetic fields. In such an LC circuit, if the capacitor contains a charge q before the switch is closed, then all the energy of the circuit is initially stored in the electric field of the capacitor. This energy is given by
2.7K
RLC Circuit as a Damped Oscillator01:30

RLC Circuit as a Damped Oscillator

1.6K
An RLC circuit combines a resistor, inductor, and capacitor, connected in a series or parallel combination.
Consider a series RLC circuit. Here, the presence of resistance in the circuit leads to energy loss due to joule heating in the resistance. Therefore, the total electromagnetic energy in the circuit is no longer constant and decreases with time. Since the magnitude of charge, current, and potential difference continuously decreases, their oscillations are said to be damped. This is...
1.6K
Design Example: Underdamped Parallel RLC Circuit01:17

Design Example: Underdamped Parallel RLC Circuit

471
Consider designing an oscillator circuit, a crucial component in various electronic devices and systems. The objective is to create an oscillator circuit with specific characteristics: a damped natural frequency of 4 kHz and a damping factor of 4 radians per second. To accomplish this, a parallel RLC circuit is employed, known for its ability to sustain oscillations at a resonant frequency. In this case, the damping factor is pivotal in achieving the desired performance.
Starting with a fixed...
471
State Space to Transfer Function01:21

State Space to Transfer Function

398
The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
The transformation process begins with the state-space representation, characterized by the state equation and the output equation. These equations are typically represented as:
398
Design Example: Capacitance Multiplier Circuit01:20

Design Example: Capacitance Multiplier Circuit

1.1K
In integrated circuit technology, a capacitance multiplier is often utilized to produce a larger capacitance value when a small physical capacitance falls short. This is achieved by a circuit that multiplies capacitance values by a factor of up to 1000, such that a 10-pF capacitor can replicate the performance of a 100-nF capacitor.
The circuit illustrated in Figure 1 below incorporates two op-amps, with the first operating as a voltage follower and the second acting as an inverting amplifier.
1.1K
Field Effect Transistor01:29

Field Effect Transistor

776
Field-effect transistors (FETs) are integral to electronic circuits and distinguished by their three-terminal setup: the gate, drain, and source. These transistors operate as unipolar devices, which utilize either electrons or holes as charge carriers, in contrast to bipolar transistors, which use both types of carriers. The primary function of the FET is to modulate the flow of these carriers from the source to the drain through a channel. The voltage difference between the gate and source...
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Related Experiment Video

Updated: Nov 11, 2025

Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators
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Quantum State Engineering of Light with Continuous-wave Optical Parametric Oscillators

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A four-state adaptive Hopf oscillator.

XiaoFu Li1, Md Raf E Ul Shougat1, Scott Kennedy1

  • 1Department of Mechanical & Aerospace Engineering, North Carolina State University, Raleigh, NC, United States of America.

Plos One
|March 25, 2021
PubMed
Summary

This study presents a novel analog adaptive oscillator (AO) capable of learning external stimulus frequency and amplitude. This four-state oscillator synchronizes without pre- or post-processing, advancing AO applications.

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Area of Science:

  • Nonlinear dynamics
  • Analog circuit design
  • Adaptive systems

Background:

  • Adaptive oscillators (AOs) are nonlinear systems with adaptable states for information encoding.
  • Previous implementations of adaptive oscillators include two-state and three-state systems using VLSI and FPGA technologies.
  • Hopf oscillators are a key type of adaptive oscillator.

Purpose of the Study:

  • To present an analog circuit implementation of a four-state adaptive oscillator.
  • To demonstrate the oscillator's ability to learn frequency and amplitude of external stimuli.
  • To verify the design through hardware measurements and simulations.

Main Methods:

  • Design and fabrication of a continuous-time, analog circuit implementation of a Hopf oscillator.
  • Hardware measurements and SPICE simulations for verification.
  • Testing the circuit's response to complex waveforms like square waves, sawtooth waves, strain gauge data, and audio signals.

Main Results:

  • The adaptive oscillator successfully learns the frequency and amplitude of external stimuli over a wide range.
  • Complete synchronization is achieved without pre- or post-processing.
  • Hardware measurements show good agreement with SPICE simulations.
  • The circuit demonstrated functionality with diverse complex waveforms.

Conclusions:

  • The developed analog adaptive oscillator offers a robust platform for learning stimulus parameters.
  • This four-state adaptive oscillator advances the capabilities of previous implementations.
  • Potential applications include robotic gait, clock oscillators, frequency analyzers, and energy harvesting.